2 The events organiser of a school sends out invitations to \(\mathbf { 1 5 0 }\) people to attend its prize day. From past experience the organiser knows that the number of those who will come to the prize day can be modelled by the distribution \(\mathbf { B } ( \mathbf { 1 5 0 } , \mathbf { 0 . 9 8 } )\).
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1. Explain why this distribution cannot be well approximated by either a normal or a Poisson distribution. [3]
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2. By considering the number of those who do not attend, use a suitable approximation to find the probability that fewer than 146 people attend. [4]